SOLUTION: If Sally can paint a house in 4 hours and John can paint the same house in 6 hours, how long will it take for both of them to paint the house together?

Algebra ->  Customizable Word Problem Solvers  -> Misc -> SOLUTION: If Sally can paint a house in 4 hours and John can paint the same house in 6 hours, how long will it take for both of them to paint the house together?      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 138190: If Sally can paint a house in 4 hours and John can paint the same house in 6 hours, how long will it take for both of them to paint the house together?
Found 2 solutions by solver91311, stanbon:
Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!
If Sally can paint the whole house in 4 hours, then she can paint 1%2F4 of the house in 1 hour. Likewise, John can paint 1%2F6 of a house in 1 hour.

Together, they can paint 1%2F4%2B1%2F6 of a house in 1 hour. So add those two fractions and take the reciprocal of the answer (invert the answer) to get the time it will take both of them to paint the house together.

You probably will want to express your answer in hours and minutes. Hint: 1%2F5 hour = 12 minutes.

Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
If Sally can paint a house in 4 hours and John can paint the same house in 6 hours, how long will it take for both of them to paint the house together?
----------------
Sally DATA:
Time = 4 hr/job ; Rate = 1/4 job/hr
------------------------
John DATA:
Time = 6 hr/job ; Rate = 1/6 job/hr
----------------------
Together DATA:
Time = x hr/job ; Rate = 1/x job/hr
--------------------------
EQUATION:
rate + rate = together rate
1/4 + 1/6 = 1/x
3x + 2x = 12
5x = 12
x = 2.4 hours (Time for them to do the job together)
OR
x = 2 hr 24 minutes (Time for them to do the job together)
=======================
Cheers,
Stan H.